Generalized Weyl Quantization, Coherent State Quantization and Time in Quantum Mechanics

In this paper we consider two quantization techniques, the generalized Weyl quan- tization and coherent state quantization using the time of arrival functions as our object of quantization. Here time of arrival functions are expressed in different phase space variables, viz. R 2 , [−π, π) × ~Z...

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Main Author: Romeo, Daisy
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Published: Archīum Ateneo 2021
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Online Access:https://archium.ateneo.edu/theses-dissertations/537
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Institution: Ateneo De Manila University
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spelling ph-ateneo-arc.theses-dissertations-16632021-10-06T05:00:04Z Generalized Weyl Quantization, Coherent State Quantization and Time in Quantum Mechanics Romeo, Daisy In this paper we consider two quantization techniques, the generalized Weyl quan- tization and coherent state quantization using the time of arrival functions as our object of quantization. Here time of arrival functions are expressed in different phase space variables, viz. R 2 , [−π, π) × ~Z and [−π, π) × R+ (forward cone). For each phase space there is a corresponding group of symmetry associated with it, and the groups are the Heisenberg group, S 1 × Z and E(2). In our quantization we also consider the different ordering schemes, both in generalized Weyl and coherent state quantizations. The computation of quantum expected values were done for both quantization methods. The novel results in this work are not only a contribution to the field of quantization but also to the field of phase space quantum mechanics. Moreover, many of the results involving coherent states are relevant to the parallel field of Signal Analysis. 2021-01-01T08:00:00Z text https://archium.ateneo.edu/theses-dissertations/537 Theses and Dissertations (All) Archīum Ateneo Coherent State Quantization, Weyl Quantization, Weyl Ordering, Sym- metric Ordering, Born-Jordan Ordering, Wigner function, Wigner Functions, Quantum Expectation Values
institution Ateneo De Manila University
building Ateneo De Manila University Library
continent Asia
country Philippines
Philippines
content_provider Ateneo De Manila University Library
collection archium.Ateneo Institutional Repository
topic Coherent State Quantization, Weyl Quantization, Weyl Ordering, Sym- metric Ordering, Born-Jordan Ordering, Wigner function, Wigner Functions, Quantum Expectation Values
spellingShingle Coherent State Quantization, Weyl Quantization, Weyl Ordering, Sym- metric Ordering, Born-Jordan Ordering, Wigner function, Wigner Functions, Quantum Expectation Values
Romeo, Daisy
Generalized Weyl Quantization, Coherent State Quantization and Time in Quantum Mechanics
description In this paper we consider two quantization techniques, the generalized Weyl quan- tization and coherent state quantization using the time of arrival functions as our object of quantization. Here time of arrival functions are expressed in different phase space variables, viz. R 2 , [−π, π) × ~Z and [−π, π) × R+ (forward cone). For each phase space there is a corresponding group of symmetry associated with it, and the groups are the Heisenberg group, S 1 × Z and E(2). In our quantization we also consider the different ordering schemes, both in generalized Weyl and coherent state quantizations. The computation of quantum expected values were done for both quantization methods. The novel results in this work are not only a contribution to the field of quantization but also to the field of phase space quantum mechanics. Moreover, many of the results involving coherent states are relevant to the parallel field of Signal Analysis.
format text
author Romeo, Daisy
author_facet Romeo, Daisy
author_sort Romeo, Daisy
title Generalized Weyl Quantization, Coherent State Quantization and Time in Quantum Mechanics
title_short Generalized Weyl Quantization, Coherent State Quantization and Time in Quantum Mechanics
title_full Generalized Weyl Quantization, Coherent State Quantization and Time in Quantum Mechanics
title_fullStr Generalized Weyl Quantization, Coherent State Quantization and Time in Quantum Mechanics
title_full_unstemmed Generalized Weyl Quantization, Coherent State Quantization and Time in Quantum Mechanics
title_sort generalized weyl quantization, coherent state quantization and time in quantum mechanics
publisher Archīum Ateneo
publishDate 2021
url https://archium.ateneo.edu/theses-dissertations/537
_version_ 1715215771905294336